Efficient soft decoding of reed-solomon codes based on sphere decoding

A novel soft-decision decoding method motivated by the idea of sphere decoding is proposed for Reed–Solomon (RS) codes. Sphere decoding reduces the complexity of finding the closest lattice point to a given point by confining the search to points that fall inside a sphere around the given point. In the authors’ proposed scheme, in order to reduce the search even further, the search effort is concentrated on the most probable lattice points. To do so, they first find the most reliable positions of the codeword. Then a sphere decoder is used to select symbol values for these positions. The proposed sphere decoder chooses the acceptable symbol values for each position from a pre-determined ordered set of most probable transmitted symbols. Each time the most reliable code symbols are selected, they are used to find the rest of RS symbols. If the resulting codeword is within the search radius, it is saved as a candidate transmitted codeword. The ordering used in the algorithm helps finding the candidate codewords quickly resulting in an efficient decoding method. Simulation results indicate considerable coding gains over hard decision decoding with a feasible complexity. The performance is also superior to the soft decision Koetter–Vardy method.